Mum-of-three Jean Evans, 68, suffered serious knife wounds.
It came just moments after a taxi driver was stabbed in Eastfield Avenue in Cambuslang at 8pm on Friday.
Mrs Evans, who was knifed in the chest in nearby Dukes Road, and taxi driver Andy Burns, 44, were rushed to Hairmyres Hospital in East Kilbride where doctors described their condition as critical but stable.
Dad-of-three Mr Burns, from Halfway, Cambuslang, was transferred to Monklands hospital in Airdrie the following day.
His face was slashed and his neck stabbed while inside his car and he suffered cuts to his hands and body as he fought off his attacker.
Police are still waiting to interview their alleged assailant who is also in hospital recovering from self-inflicted injuries after an apparent suicide attempt.
Mrs Evans's next door neighbour Maureen Kenny, 77, said lives with her son Stephen and used to run a cafe in the Barras.
She said: "The first I noticed was all the police cars, there were people all rushing about.
"I saw a neighbour come across with a duvet and then I went outside and saw Jean being stretchered into an ambulance.
"I saw blood all down the path and then later realised she must have been trying to reach me to get help.I spoke to her on Stephen and he said the family is still in shock."